This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A381485 #5 Feb 25 2025 02:29:54 %S A381485 6,0,0,9,2,5,2,1,2,5,7,7,3,3,1,5,4,8,8,5,3,2,0,3,5,4,4,5,7,8,4,1,5,9, %T A381485 9,1,0,4,1,8,8,2,7,6,2,3,0,7,5,4,1,0,3,5,4,5,1,7,4,2,1,7,6,0,3,7,8,6, %U A381485 1,1,5,8,0,4,8,8,3,5,0,7,4,2,0,0,7,6,9,8,4,7,0,0,3,0,8,1,7,8,6,2,7,8,9,1,9 %N A381485 Decimal expansion of sqrt(13)/6. %C A381485 The greatest possible minimum distance between 6 points in a unit square. %C A381485 The solution was found by Ronald L. Graham and reported by Schaer (1965). %D A381485 Hallard T. Croft, Kenneth J. Falconer, and Richard K. Guy, Unsolved Problems in Geometry, Springer, 1991, Section D1, p. 108. %D A381485 Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, Vol. 94, Cambridge University Press, 2003, Section 8.2, p. 487. %H A381485 J. Schaer, <a href="https://doi.org/10.4153/CMB-1965-018-9">The densest packing of 9 circles in a square</a>, Canadian Mathematical Bulletin, Vol. 8, No. 3 (1965), pp. 273-277. %H A381485 D. Würtz, M. Monagan, and R. Peikert, <a href="https://www.cecm.sfu.ca/~mmonagan/papers/CirclePacking.pdf">The history of packing circles in a square</a>, Maple Technical Newsletter, Vol. 1 (1994), pp. 35-42; <a href="https://www.researchgate.net/publication/228326618_The_History_of_Packing_Circles_in_a_Square">ResearchGate link</a>. %H A381485 <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>. %F A381485 Equals A010470 / 6 = A295330 / 3 = A344069 / 2 = A176019 - 1/2 = sqrt(A142464). %F A381485 Minimal polynomial: 36*x^2 - 13. %e A381485 0.60092521257733154885320354457841599104188276230754... %t A381485 RealDigits[Sqrt[13] / 6, 10, 120][[1]] %o A381485 (PARI) list(len) = digits(floor(10^len*quadgen(52)/6)); %Y A381485 Solutions for k points: A002193 (k = 2), A120683 (k = 3), 1 (k = 4), A010503 (k = 5), this constant (k = 6), A379338 (k = 7), A101263 (k = 8), A020761 (k = 9), A281065 (k = 10). %Y A381485 Cf. A010470, A142464, A176019, A295330, A344069. %K A381485 nonn,cons,easy %O A381485 0,1 %A A381485 _Amiram Eldar_, Feb 24 2025